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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1071 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj69 34674. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1071.7 | ⊢ 𝐷 = (ω ∖ {∅}) |
Ref | Expression |
---|---|
bnj1071 | ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1071.7 | . . 3 ⊢ 𝐷 = (ω ∖ {∅}) | |
2 | 1 | bnj923 34432 | . 2 ⊢ (𝑛 ∈ 𝐷 → 𝑛 ∈ ω) |
3 | nnord 7884 | . 2 ⊢ (𝑛 ∈ ω → Ord 𝑛) | |
4 | ordfr 6389 | . 2 ⊢ (Ord 𝑛 → E Fr 𝑛) | |
5 | 2, 3, 4 | 3syl 18 | 1 ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 ∈ wcel 2098 ∖ cdif 3946 ∅c0 4326 {csn 4632 E cep 5585 Fr wfr 5634 Ord word 6373 ωcom 7876 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2706 df-cleq 2720 df-clel 2806 df-ral 3059 df-rab 3431 df-v 3475 df-dif 3952 df-in 3956 df-ss 3966 df-uni 4913 df-tr 5270 df-po 5594 df-so 5595 df-fr 5637 df-we 5639 df-ord 6377 df-on 6378 df-om 7877 |
This theorem is referenced by: bnj1030 34651 bnj1133 34653 |
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